As a kid, I watched Three's Company in its original run and thought it was hilarious. In my late teens/early twenties, I thought it was an overblown, overwrought comedy and was ashamed I ever watched it. Now, when I see reruns in my thirties, I realize that all the actors involved were intentionally being Large Hams, and I think it's hilarious. — Devil's Advocate
To answer a question on the main page as to why the girls keep Jack around: in The Seventies men typically made a lot more than women at any given job, and could count on greater stability of employment (as they were perceived as the breadwinners). Even though Jack can't at the moment afford to live on his own, he still brings more money to the table than a potential female roommate (once he finishes cooking school and gets a job as a chef, the money gets even better). And a gay man would eventually be outed, which wouldn't be good for anyone involved (especially the man back then).
In the pilot, Janet and Chrissy's roommate Eleanor is leaving the apartment because she's getting married...and it's made clear (via Jack's dialogue) that she went into labor at her going-away party. When she returns sometime later in the episode "Eleanor's Return", it is revealed that she's getting a divorce and moving to a new city to start over. However, no mention is made of a child. Now, one could assume that the marriage didn't work out because it was one of necessity rather than love, but the fact that the baby that (presumably) caused the wedding in the first place isn't present or even discussed could only mean one of two things:
The ex-husband got custody of the child. Unlikely, given the time period. But if he did, that means that Eleanor must have had some fairly serious issues that prevented her from taking care of her child (and there are occasional mentions within the show supporting the idea of her being a bit "wild" during her time in the apartment). It is possible her parents are simply taking care of the child while she settles into her new life, but again this is never mentioned or explained either.
Just as likely, especially for the time period, is that the child was taken by social services (possibly as a consequence of Eleanor's "wild" behavior, or something much darker). Reunification with birth parents wasn't nearly the priority for social services back then as it is today, so chances are Eleanor wouldn't see the child again until he/she was an adult and sought her out. The embarrassment to Eleanor and the discomfort everyone else feels over the situation would be enough to avoid discussion in polite company.
Eleanor had a miscarriage (possibly after leaving the party mentioned in the pilot) or the child passed on at some other later date, thus destroying the marriage. And her roommates are well aware of what happened to the baby, which is why the matter is never brought up and why they don't appear too surprised to hear about the divorce.
Either way, heavy stuff for a light-hearted sitcom.
So both Mr. Roper and Mr. Furley had an issue with a (straight) man "living in sin" with two women, but neither of him had any sort of issues with Larry's parade of women? What - pre-marital hanky panky is okay as long as you're not living together?.
Possible they just didn't realize it. It's much easier to hide it when the women leave and don't hang around the apartment. As long as he kept up with his rent and didn't make too much noise they never seemed to pay much attention to what Larry did.
The entire cast of characters seem to subscribe to the "out of sight, out of mind" theory of personal relationships: if a particular person is not actively and physically present in that character's life at that moment, that person might as well not exist. It would help to explain why so many characters just completely disappear from the characters' lives that should otherwise have some continued presence. This is most glaring in the series finale with Janet's wedding: it's more notable who's absent from the wedding than who's there. The Ropers, Chrissy, Cindy, Janet's parents, and her sister (all of whom have been featured on the show to varying amounts) fail to take part in the biggest day of Janet's life.